Estimate the crystallite size of the given nanomaterial using p-XRD data:Peak position θ = 10.81o, FWHM of sample = 1.8o, k = 0.88 and λ = 1.54 Å
Question
Estimate the crystallite size of the given nanomaterial using p-XRD data:Peak position θ = 10.81o, FWHM of sample = 1.8o, k = 0.88 and λ = 1.54 Å
Solution
To estimate the crystallite size of the given nanomaterial using p-XRD data, we can use the Scherrer equation:
D = kλ / (β cos θ)
where: D is the crystallite size, k is the shape factor (dimensionless), usually taken as 0.9, λ is the X-ray wavelength, β is the full width at half maximum (FWHM) in radians, θ is the Bragg angle in radians.
Given: Peak position θ = 10.81o, FWHM of sample = 1.8o, k = 0.88, λ = 1.54 Å.
First, we need to convert the angles from degrees to radians. We know that π radians = 180 degrees. So, to convert degrees to radians, we multiply by π/180.
θ = 10.81 * π/180 = 0.1886 radians, β = 1.8 * π/180 = 0.0314 radians.
Now, we can substitute these values into the Scherrer equation:
D = 0.88 * 1.54 / (0.0314 * cos(0.1886)) = 44.8 Å.
So, the estimated crystallite size of the given nanomaterial is approximately 44.8 Å.
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